Kiran is correct. (I agree with Kiran.)
_____
Suppose the length and width are L and W. The Pythagorean theorem says the diagonal distance is ...
... d = √(L² +W²)
If the dimensions are doubled, the the diagonal distance becomes ...
... D = √((2L)² +(2W)²) = √(4(L² +W²)) = 2√(L² +W²)
... D = 2d
Answer:
Kiran's statement is correct.
Step-by-step explanation:
Kiran says that if the field were twice as long and twice as wide, then it would be twice the distance to the far corner.
Let the original length be = l
Let the original width be = w
Let the original diagonal be = d1
As per Pythagoras theorem,
[tex]d1^{2} =l^{2} +w^{2}[/tex]
When the dimensions are twice the original;
Length = 2l
Width = 2w
Diagonal = d2
We get the formula :
[tex]d2^{2} =2l^{2} +2w^{2}[/tex]
[tex]d2^{2} =2(l^{2} +w^{2})[/tex]
Or [tex]d2^{2} =2d1^{2}[/tex]
So, we can say that Kiran is correct.
choose the best response to explain why 3 (x+12)=3 (x+5)
3(x + 12) does not, and never will, equal 3(x + 5)
We can solve the equation to verify.
3(x + 12) = 3(x + 5)
Distributive property.
3x + 36 = 3x + 15
Subtract 15 from both sides.
3x + 21 = 3x
Cancel like terms.
21 = 0 × this is incorrect.
If f is a polynomial function and xminus−5 is a factor of f, then f(5)equals=_______.
if (x - 5 ) is a factor of f(x ) then x = 5 is a root of f(x) and f(5) = 0
Answer:
[tex]f(5) = 0[/tex]
Step-by-step explanation:
A function [tex]f[/tex] can be simplified by it's roots.
For example, a second order function expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0.[/tex]
Can be expressed in function of it's roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = (x - x_{1})*(x - x_{2})[/tex].
Is [tex]x-5[/tex] is a factor of f, this means that f can be expressed in function of [tex]x - 5[/tex], that is, x = 5 is a root of the equation.
This means that:
[tex]f(5) = 0[/tex]
9y + 3 > 4y - 7
thats it
Need help with this please
An Uber fare in Columbus is $3.50 for the first ½ mile and additional mileage charged at a rate of $0.30 for each additional 0.1 mile. You plan to give the driver a $2 tip. How many miles can you ride for $15? Please show or explain your calculations.
If we consider the first half mile to be charged at $0.30 per tenth also, that half-mile costs $1.50 and the charges amount to a fixed fee of $2.00 and a variable fee of $0.30 per tenth mile.
After you subtract the $2 tip and the fixed $2 fee from the trip budget amount, you have $11.00 you can spend on mileage charges. At 0.30 per tenth mile, you can travel
... $11.00/$0.30 = 36 2/3 . . . . tenth-miles
The trip is measured in whole tenths, so you can ride ...
... 36 × 1/10 = 3.6 miles
_____
If you want to see this in the form of an equation, you can let x represent the miles you can travel. Then your budget amount gives rise to the inequality ...
... 3.50 + 0.30((x -.50)/0.10) + 2.00 ≤ 15.00
... 3.50 + 3x -1.50 +2.00 ≤15.00 . . . . . . . eliminate parentheses
... 3x ≤ 11.00 . . . . . . . . . . . . . . . . . . . . . . . . collect terms, subtract 4
... x ≤ 11/3 . . . . . . . . . . . . . . . . . . . . . . . . . . divide by 3
... x ≤ 3.6 . . . . . rounded down to the tenth
Suppose that you are asked if there would be a strong or weak correlation between the number of people shopping in malls and the approach of the Holiday Season. Explain whether there would be a strong or weak correlation and the difference between the two.
There could be a strong correlation between the proximity of the holiday season and the number of people who buy in the shopping centers.
It is known that when there are vacations people tend to frequent shopping centers more often than when they are busy with work or school.
Therefore, the proximity in the holiday season is related to the increase in the number of people who buy in the shopping centers.
This means that there is a strong correlation between both variables, since when one increases the other also does. This type of correlation is called positive. When, on the contrary, the increase of one variable causes the decrease of another variable, it is said that there is a negative correlation.
There are several coefficients that measure the degree of correlation (strong or weak), adapted to the nature of the data. The best known is the 'r' coefficient of Pearson correlation
A correlation is strong when the change in a variable x produces a significant change in a variable 'y'. In this case, the correlation coefficient r approaches | 1 |.
When the correlation between two variables is weak, the change of one causes a very slight and difficult to perceive change in the other variable. In this case, the correlation coefficient approaches zero
Most likely, there would be a strong correlation between the two.
A correlation is a measurement of the relationship between two variables. When two variables are strongly correlated, this means that a change in one variable has a strong impact on the other one. On the other hand, when the correlation between variables is weak, this means that the two variables are not strongly connected. In this example, the two situations are likely to be strongly correlated because the number of people is very likely to go up as the holiday season approaches.
Ruben said that 96.52 ÷ 12.7 equals 7.6.
Is Ruben's answer reasonable?
A.
No, Ruben's answer should be closer to 0.8.
B.
No, Ruben's answer should be closer to 80.
C.
No, Ruben's answer should be closer to 800.
D.
Yes, Ruben's answer is reasonable.
By rounding to the nearest whole numbers and estimating, it is confirmed that Ruben's answer of 96.52 ÷ 12.7 equals 7.6 is indeed reasonable.
Explanation:To assess if Ruben's answer that 96.52 ÷ 12.7 equals 7.6 is reasonable, let's consider the magnitude of the numbers involved. Firstly, we can simplify our estimation by rounding the numbers to the nearest whole digits, which gives us approximately 97 ÷ 13. By using division, we see that 13 goes into 97 about 7 times with some remainder, since 13 x 7 is 91, which is close to 97.
Now, 7.6 is indeed close to our estimation, so we can determine that Ruben's answer is within a reasonable range. Thus, the correct response to whether Ruben's calculation is reasonable would be:
D. Yes, Ruben's answer is reasonable.
How do you write 300450390 in expanded form
300000000+400000+50000+300+90= 300450390
Hope this helped! :)
How do you write 300450390 in expanded form ?
300000000+ 400000+ 50000+ 300+ 90= 300450390
Hope this helps. If it does, please mark me brainiest! <3
A selection of staff wages is collected and shown below. £254 £254 £310 £276 £116 £90 £312 £180 £180 £536 £350 £243 £221 £165 £239 £700 What is the mode of staff wages? £ and £
the mode is the amount/s which occurs most frequently.
In this data set there are 2 values which occur twice
the mode is £254 and £180
The mode of staff wages is:
£ 180 and £ 254
Step-by-step explanation:The mode of a data set is a data value that exist or occur in the set most frequently (i.e. most of the times)
We are given data points as:
£254 £254 £310 £276 £116 £90 £312 £180 £180 £536 £350 £243 £221 £165 £239 £700
On arranging these data points along with their frequency we get:
Data point Frequency
£90 1
£116 1
£165 1
£180 2
£221 1
£239 1
£243 1
£254 2
£276 1
£310 1
£312 1
£350 1
£536 1
£700 1
Two data points has highest frequency
£180 and £254
( since both have frequency 2)
Which expression is equivalent to the expression -2 4/5+6/7: 2 4/5-6/7: -2 4/5-6/7: -(2 4/5+6/7): -(2 4/5 - 6/7)
When you factor out -1, you get ...
... -(2 4/5 - 6/7)
it takes Jupiter 11.9 years to orbit,or go around the sun. Saturn takes 17.6 more years than Jupiter to orbit the sun. About how long does it take Saturn to orbit the sun?
Saturn takes 17.6 more years than Jupiter, so 17.6 + 11.9 will get you how long Saturn will take to orbit the sun, which would give you 29.5 years.
The time it takes Saturn to orbit the sun can be calculated by adding Jupiter's orbit time to the additional time Saturn takes after Jupiter. Saturn takes approximately 29.5 years to complete one orbit around the sun.
To find out how long it takes Saturn to orbit the sun, we know that Jupiter takes 11.9 years and Saturn takes 17.6 more years than Jupiter. So, Saturn takes 11.9 + 17.6 = 29.5 years to orbit the sun.
Find a gradient of a line that is parallel and perpendicular to this line with this gradient of -2
a gradient of a line that is parallel and perpendicular to this line with this gradient of -2
Gradient is the slope
So slope of the line =-2
Slope of parallel line is equal to the slope of the line
So slope of parallel line = -2
Slope of perpendicular line is equal to negative reciprocal of slope of the line
We know slope of line = -2
Negative reciprocal = [tex]\frac{1}{2}[/tex]
So , Slope of perpendicular line= [tex]\frac{1}{2}[/tex]
City A and city B each have 10 parks. The table shows the number of acres for each park in the two cities. City A 6 9 10 7 10 10 2 5 8 8 City B 5 10 8 11 7 12 6 5 4 5 Select from the drop-down menus to correctly complete each statement. The mean number of acres for each park for the two cities is . The range for the number of acres for parks for the two cities is .
Answer:
The mean number of acres for each park for the two cities is:
City A: 7.5
City B: 7.3
The range for the number of acres for parks for the two cities is : 8
Step-by-step explanation:
The table shows the number of acres for each park in the two cities.
City A: 6 9 10 7 10 10 2 5 8 8
City B : 5 10 8 11 7 12 6 5 4 5
City A:
Minimum acre of park=2
Maximum acre of park=10
Range=Maximum-Minimum
Range=10-2
Range=8
Now mean is calculated as:
[tex]Mean=\dfrac{6+9+10+7+10+10+2+5+8+8}{10}\\\\\\Mean=\dfrac{75}{10}\\\\Mean=7.5[/tex]
City B:
Minimum acre of park=4
Maximum acre of park=12
Range=Maximum-Minimum
Range=12-4
Range=8
Now mean is calculated as:
[tex]Mean=\dfrac{5+10+8+11+7+12+6+5+4+5}{10}\\\\\\Mean=\dfrac{73}{10}\\\\Mean=7.3[/tex]
Answer:
1. about the same
2. the same
Step-by-step explanation:
The solution to w/-7=-21 is 3 true or false
false , w = 147
multiply both sides by - 7 to eliminate the fraction
w = - 7 × - 21 = 147
The solution to the equation w/-7=-21 is not 3 but 147. Therefore, the original statement is false.
Explanation:The equation in question is w/-7 = -21. To solve this equation, we multiply both sides by -7.
When we do this, the equation simplifies to w = -(-21)*7. As -(-21) turns to 21, and 21*7 is equal to 147, we find that the solution to the equation w/-7=-21 is w=147, and not w=3.
Therefore, the statement 'The solution to w/-7=-21 is 3' is false.
Learn more about Equation Solution here:https://brainly.com/question/545403
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Use substitution to solve the linear system of equations
x = 4.
-y = 1/2x
(4, -2)
(-2, 4)
(4, 2)
(2, -4)
solution = (4, - 2 )
substitute x = 4 into - y = [tex]\frac{1}{2}[/tex] x
- y = [tex]\frac{1}{2}[/tex] × 4 = 2 ( multiply both sides by - 1 )
y = - 2
solution is ( 4, - 2 )
Answer:
I think it is (4,-2)
Katrina drinks 0.5 gallons of water per day. Which expression shows how to find the number of cups of water she drinks in a week?
There are 16 cups in a gallon.
× ×
× ×
× ×
× ×
Answer:
Expression Katrina drinks of water in 7 day = 8 *7 cups .
Step-by-step explanation:
Given : Katrina drinks 0.5 gallons of water per day and There are 16 cups in a gallon.
To find : Which expression shows how to find the number of cups of water she drinks in a week.
Solution : We have given that
Katrina drinks of water per day = 0.5 galoons.
1 gallon = 16 cup .
So, Katrina drinks of water per day = 0.5 * 16 cups.
Katrina drinks of water per day = 8 cups.
1 week = 7 days .
Katrina drinks of water in 7 day = 8 *7 cups.
Katrina drinks of water in 7 day = 56 cups.
Therefore, Expression Katrina drinks of water in 7 day = 8 *7 cups .
Find the linearization L(x) of the function at a. f(x) = x^4 + 2x^2, a = 1
The equation of the tangent line at x=1 can be written in point-slope form as
... L(x) = f'(1)(x -1) +f(1)
The derivative is ...
... f'(x) = 4x^3 +4x
so the slope of the tangent line is f'(1) = 4+4 = 8.
The value of the function at x=1 is
... f(1) = 1^4 +2·1^2 = 3
So, your linearization is ...
... L(x) = 8(x -1) +3
or
... L(x) = 8x -5
1/2divide by 5 =1 blank of 1/2
Answer:
i am pretty sure that it is .2,
Step-by-step explanation:
first, you would do .5 divided by 5 which is 0.1. Then you would do 0.1 divided by 0.5 and you would get 0.2
In figure, MN : NP = 9:1. If MP = 2. Find the distance from M to point K that is 1/4 the distance from M to N?
(A) 1 (B) 1 1/3 (C) 9/20 (D) 1 8/10
The distance MN is 9/(9+1) = 9/10 of the distance MP, so is
... MN = (9/10)×MP = (9/10)×2 = 9/5
The distance MK is 1/4 that, so is ...
... MK = (1/4)×(9/5) = 9/20 . . . . . matches selection (C)
Answer:
C
Step-by-step explanation:
the answer is C. give the person the brainly :) ignore this answer
If y varies directly with x, write an equation for the direct variation. Then find the value.
If y=3 when x=2, find y when x=1
Plz show work
since y varies directly with y then
y = kx ( k is the constant of variation )
to find k use y = 3 when x = 2
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{3}{2}[/tex]
equation is : y = [tex]\frac{3}{2}[/tex] x
When x = 1 then y = [tex]\frac{3}{2}[/tex] × 1 = [tex]\frac{3}{2}[/tex]
[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we also know that}~~ \begin{cases} y=3\\ x=2 \end{cases}\implies 3=k2\implies \cfrac{3}{2}=k \\\\\\ therefore\qquad \boxed{y=\cfrac{3}{2}x} \\\\\\ \textit{when x = 1, what is \underline{y}?}\qquad y=\cfrac{3}{2}(1)\implies y=\cfrac{3}{2}[/tex]
Dad, Anna, and Todd are walking in a city park together. While dad made 3 steps, Anna made 5 steps. For every 3 of Anna's steps, Todd made 5 steps. Anna and Todd calculated that they did 400 steps together. How many steps did dad make during that period?
Answer:
Dad made 90 steps during that period.
Step-by-step explanation:
Let x,y,z be the steps made by dad,Anna and Todd.
Given that while dad made 3 steps, Anna made 5 steps.
That is [tex]\frac{x}{y}= \frac{3}{5}[/tex]
[tex]y=\frac{5x}{3}[/tex]
And for every 3 steps Anna made, Todd made 5 steps.
That is [tex]\frac{y}{z}= \frac{3}{5}[/tex]
[tex]z=\frac{5y}{3} =\frac{5(\frac{5x}{3}) }{3} =\frac{25x}{9}[/tex]
It is also given that total number of steps made by Anna and Todd is 400.
That is y+z=400
let us plugin y and z in terms of x.
[tex]\frac{5x}{3} +\frac{25x}{9} =400[/tex]
[tex]\frac{15x}{9} +\frac{25x}{9}=400[/tex]
[tex]\frac{40x}{9}=400[/tex]
[tex]x=400X\frac{9}{40} =90steps[/tex]
Hence Dad made 90 steps during that period.
Select all the proper fractions
5/3
6/7
12/17
9/5
11/4
6/25
6/7 and 12/17 all the other have to be reduced
These are the proper fractions
6/7
12/17
6/25
These are improper fraction
5/3
9/5
11/4
solve 0.7cos(x)-sin(x)=r for x
where r is a real number
show all steps (if you don't show steps, I'll report the answer)
Try this solution (see the attachment), note:
1. the word 'ctgx' means 'cotangens x'; 2. this equation has roots not for all the real number 'r', it is shown in the 2-d line of the answer; 3. the answer is marked with red colour.
Answer "and" Explanation:
You know that [tex]sin^{2} + cos^{2} x = 1[/tex], so with the given information, you can write
[tex](\frac{7}{10} cos/x-r)^{2} + cos^{2} x= 1[/tex]
that becomes
[tex]\frac{149}{100} cos^{2} / x- \frac{7}{5} r / cos /x + r^{2} - 1 = 0[/tex]
or as well
[tex]149cos^{2} / x -140r / cos / x + 100(r^{2} - 1) = 0[/tex]
The condition for this equation to have real roots is
[tex]70^{2} r^{2} - 149 x 100^{2} (r^{2} - 1) \geq 0[/tex]
hence [tex]r^{2} \leq 149/ 100[/tex]
The roots of the quadratic equation [tex]149t^{2} - 140rt + 100(r^{2} - 1) = 0[/tex] are in the interval [- 1, 1], because with the limitation [tex]|r| \leq \sqrt{149/100}[/tex], the point of a minimum of the polynomial lies between - 1 and 1. Moreover, the polynomial evaluated at - 1 and 1 is > 0 for every r.
Solve for cos x and find the value of sin x.
It was -8 degrees in the morning, but by 5pm the temperature decreased 10 degrees. What was the temperature then?
Please Answer The Following Questions.
Answer:
4. 73
5. 40°
Step-by-step explanation:
The sum of the angles in a triangle is 180°. The sum of angles in a linear pair is 180°.
4. 45° +62° + k° = 180°
... 107 +k = 180 . . . . . collect terms, divide by °
... k = 180 -107 = 73 . . . . . subtract 107
_____
5. ∠STR = ∠SRT = 20°
... ∠STR +∠STU = 180°
... 20° + 4x = 180°
... 4x = 160° . . . . . . . . subtract 20°
... x = 40° . . . . . . . . . . divide by the coefficient of x
For the following system of inequalities, which point lies in the solution set?
4x + 2y > 12
x − y > 5
Select one:
A. (1,1)
B. (8,4)
C. (3,9)
D. (9,1)
D
Substitute the coordinates of the given points into the inequalities and if both are true then the point is a solution to the system.
A(1, 1 ) : 4 + 2 = 6 and 1 - 1 = 0 not a solution
B(8, 4 ) : 32 + 8 = 40 and 8 - 4 = - 4 not a solution
C(3, 9 ) : 12 + 18 = 30 and 3 - 9 = - 6 not a solution
D(9, 1 ) : 36 + 2 = 38 and 9 - 1 = 8 is a solution
the point (9, 1 ) is the only point that makes both inequalities true
Need help on this please
If f(x) = 5x - 2 and g(x) = 2x + 1, find (f - g)(x)
(5x - 2 - g(x))(x)
(5x - 2 -(2x + 1)
(5x - 2 - (2x + 1) : 3x - 3
= 3x - 3
PLEASE HELP QUICK
Mike was in charge of collecting contributions for the Food Bank. He received contributions of $13, $34, $26, $31, and $28 from five co-workers. Find the median value of these contributions.
median = $28
the median is the middle value of the data arranged in ascending order
rearrange the data in ascending order
13 26 28 31 34
the middle entry is 28
hence median = $28
The median is the middle value so put the numbers in order from smallest to largest.
13,26,28,31,34
The middle value is 28, so the median value is 28
X(x+3)-x=5 is a quadratic equation?
True
False
The given equation can be simplified to ...
... x² +2x = 5
This is a quadratic equation. The highest-degree term has degree 2. (TRUE)